132 
the mean potential between the droplet and the outside 
air approached 60 mv. By estimating the total charge 
resulting from the association of typical cloud elements, 
relatively large free charges per droplet were calcu- 
lated. It was found that precipitation electrical phenom- 
ena could be well deseribed, both qualitatively and 
quantitatively, by such an hypothesis. The theory is 
not considered complete but it does serve to emphasize 
the probable importance of association mechanisms 
in the production of highly charged precipitation. 
Separation of Free Electrical Charges and the Impor- 
tance of Droplet Size 
Although all matter is composed of an enormous 
number of electrical charges, it 1s a general rule that 
every small volume of space contains as many positive 
charges as negative charges. A short calculation will 
show that this mdeed must be the case, because any 
systematic separation of charges of opposite sign im- 
mediately sets up surprisingly large electrical forces 
that always act in such a direction as to restore elec- 
trical neutrality. 
An important exception to the general rule of neu- 
trality occurs in the earth’s atmosphere when free 
charges of one sign become selectively attached to the 
larger or smaller precipitation elements. As an example, 
suppose that, for some reason, all of the elementary 
cloud particles in a given volume selectively capture a 
positive (or negative) charge. When rain is formed, 
these cloud particles associate to form a highly charged 
raindrop. Suppose that, simultaneously, neutralizing 
negative (or positive) charges for each droplet are 
immediately outside and are attached to air molecules 
or other very small molecular aggregates. Gravity acts 
on both types of charged carrier, and they fall at a 
velocity determined by the acting aerodynamic and 
electrical forces. When the droplets are small, so that 
gravity does not give the particles high velocities, the 
neutralizing negative (or positive) charges are carried 
along with the fallmg positive (or negative) droplets 
as a result of electric fields. Thus, after a preliminary 
small separation, gross separations of the type ob- 
served in thunderstorms do not result. 
Unfortunately, the literature does not contain an 
adequate discussion of the important problem of charge 
separation as influenced by the size of the droplet. 
Since the droplet size and the acting forces are of the 
utmost importance in understanding charge separation 
and lightning processes in the atmosphere, it has seemed 
worth while to discuss this matter here. 
Consider a cloud of mfinite extent, lying parallel to 
the earth’s surface and composed of but two types of 
particles: (1) ramdrops upon which positive charge, for 
example, is selectively deposited; (2) particles (as- 
sumed to be small) with a sufficient number of them 
carrying a total charge just large enough to neutralize 
the positive charge on the rain droplets. Assume, at 
first, that the whole cloud system contains exactly as 
much positive electricity as negative, each uniformly 
distributed. It will therefore be neutral and no electric 
fields will exist. 
ATMOSPHERIC ELECTRICITY 
It is noted first that an electric field produced by 
the separation of charges always acts in such a direc- 
tion as to prevent the separation. Thus, if positively 
charged droplets fall with respect to negatively charged 
droplets, the electric field thus produced acts to support 
raindrops while simultaneously it drags the small nega- 
tive elements downward. 
It is clear that the electric field can never grow to 
exceed a value greater than that of the field which will 
support the droplet. Thus, if #, is the electric field 
when the droplets are completely supported by it, q is 
the charge on the droplet and m is its mass, while g is 
the acceleration due to gravity, one may equate the 
electrical and gravitational forces and write 
mg 
B= (1) 
This electric field is an absolute maximum im the at- 
mosphere for droplets of a given size and is large 
enough in general to cause spark discharges. 
The equilibrium electric field #,,, described above, is 
never realized practically because of the conductivity 
of the earth’s atmosphere, which always acts to dis- 
charge and reduce any electric field so produced. In 
order that one may formulate quantitatively the actual 
equilibrium when the droplets are allowed to fall m an 
electrically conducting atmosphere, a one-dimensional 
solution will be obtained by considering the transfer of 
charge within a prism one square centimeter in cross 
section and extending vertically through the cloud. The 
electric current per unit area, 7, due to the convected 
charges on the precipitation, is 
i= 2) (myqy04 + ng), (2) 
where n is the number of charged particles per unit 
volume, g the charge on each particle, and v the veloc- 
ity of fall, and where the subscripts denote the sign of 
the transported charge. This downwardly transported 
net free charge per unit time, 7, not only charges the 
conducting earth below but also supplies charge to re- 
place that conducted upward as a result of the normal 
ionic conductivity of the atmosphere and the generated 
electric field. If Q is the total free charge per unit area 
deposited on the surface of the earth, then, equating 
the rate of supply to the rate of loss of charge, one has 
dQ 
a + oH = 7 (nigy04 + n-g0_), (3) 
where o is the normal ionic conductivity of the earth’s 
atmosphere, and # is the electric field generated by 
the charge separation. Under the assumed geometrical 
conditions, the surface charge density Q is related to 
the produced electric field # by the relation 
EH = 47Q, (4) 
from which one may write, for regions near the earth’s 
surface, that 
1 dz 
ane ae D (m49404 + ng). (5) 
